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DY: Dynamik und Statistische Physik

DY 25: Symposium Renormalization and Scaling (SYRS) – Contributed Talks II

DY 25.1: Vortrag

Samstag, 5. März 2005, 16:00–16:15, TU H3010

The scaling of a self-avoiding walk on a percolation cluster — •Yurij Holovatch^1,2,3, Viktoria Blavats’ka¹, Christian von Ferber⁴, and Reinhard Folk² — ¹Institute for Condensed Matter Physics, UA-79011 Lviv, Ukraine — ²Institut für Theoretische Physik, Johannes Kepler Universität Linz, A-4040 Linz, Austria — ³Ivan Franko National University of Lviv, UA-79005 Lviv, Ukraine — ⁴Theoretische Polymerphysik, Universität Freiburg, D-79104 Freiburg, Germany

The scaling properties of a self-avoiding walk (SAW) on the d-dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Meir and Harris [1]. Although the former one-loop analysis points to a new universality class for a SAW on the percolation cluster, the numerical values found for the scaling exponents almost coincide with those for a SAW on an undiluted lattice. Our second order result for the mean square end-to-end distance exponent reads: ν_p=1/2+ε/42+ 110ε²/21³, ε=6−d and leads to perfect agreement with known theoretical, MC and exact enumeration data [2,3]. Moreover, we argue that the observed scaling possesses multifractal properties and obtain a non-trivial spectrum of correlation exponents governing the multifractal scaling.

[1] Y. Meir and A.B. Harris, Phys. Rev. Lett. 63, 2819 (1989).

[2] C. von Ferber, V. Blavats’ka, R. Folk, Yu. Holovatch, Phys. Rev. E 70 035104(R) (2004).

[3] V. Blavats’ka, C. von Ferber, R. Folk, Yu. Holovatch, in: Polymers in Random Media, ed. by B. Chakrabarti, Elsevier, 2005 (to appear).